The realization space is
  [1   0   1   0   1    0         1      x1 - 1             x1 - 1   2*x1^2 - 2*x1 + 1               x1 - 1]
  [0   1   1   0   0    1         1         -x1                -x1                  x1   -2*x1^2 + 2*x1 - 1]
  [0   0   0   1   1   -1   -x1 + 1   x1^2 - x1   -x1^2 + 2*x1 - 1     x1^2 - 2*x1 + 1            x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (12*x1^10 - 68*x1^9 + 179*x1^8 - 290*x1^7 + 318*x1^6 - 243*x1^5 + 129*x1^4 - 46*x1^3 + 10*x1^2 - x1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1 - 1, x1^2 - x1 + 1, x1, 2*x1^2 - 2*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1, x1 - 2, x1^2 - 3*x1 + 1]